Learning Math: Geometry, a video- and Web-based course for elementary and middle school teachers, introduces geometric reasoning as a method for problem-solving. In this course, which is organized around the content standards of the National Council of Teachers of Mathematics (NCTM), you will explore the properties of geometric figures; make constructions using pencil and paper, and also using dynamic software; and practice using mathematical language to express ideas and justify your reasoning. Some important geometric ideas, such as symmetry, similarity, and trigonometry, will also be examined. You will begin to explore the basis of formal mathematical proofs and solid geometry. The course material progresses from more visual, intuitive ways of solving problems to more formal explorations of geometric ideas, properties, and proofs.

The course consists of 10 approximately two-and-a-half-hour sessions, each with a half hour of video programming, problem-solving activities provided online and in a print guide, and interactive activities and demonstrations on the Web. The 10th session (choose video program 10 or 11 and 12, depending on your grade level) explores ways to apply the concepts of geometry you've learned in your own classroom.

Video 1. What Is Geometry?
Explore the basics of geometric thinking using rich visualization problems and mathematical language. Use your intuition and visual tools for geometric construction. Reflect on the basic objects of geometry and their representation. Go to this unit.

Video 2. Triangles and Quadrilaterals
Learn about the classifications of triangles, their different properties, and relationships between them. Examine concepts such as triangle inequality, triangle rigidity, and sidesideside congruence, and look at the conditions that cause them. Compare how these concepts apply to quadrilaterals. Explore properties of triangles and quadrilaterals through practical applications such as building structures. Go to this unit.

Video 3. Polygons
Explore the properties of polygons through puzzles and games, then proceed into a more formal classification of polygons. Look at mathematical definitions more formally, and explore how terms can have different but equivalent definitions. Go to this unit.

Video 4. Parallel Lines and Circles
Use dynamic geometry software to construct figures with given characteristics, such as segments that are perpendicular, parallel, or of equal length, and to examine the properties of parallel lines and circles. Look past formal definitions and discover the properties and relationships among geometric figures for yourself. Go to this unit.

Video 5. Dissections and Proof
Review and explore transformations such as translation, reflection, and rotation. Apply these ideas to solve more complex geometric problems. Use your knowledge of properties of figures to reason through, solve, and justify your solutions to problems. Analyze and prove the midline theorem. Go to this unit.

Video 6. Pythagorean Theorem
Continue to examine the idea of mathematical proof. Look at several geometric or algebraic proofs of one of the most famous theorems in mathematics: the Pythagorean theorem. Explore different applications of the Pythagorean theorem, such as the distance formula. Go to this unit.

Video 7. Symmetry
Investigate symmetry, one of the most important ideas in mathematics. Explore geometric notions of symmetry by creating designs and examining their properties. Investigate line symmetry and rotation symmetry; then learn about frieze patterns. Go to this unit.

Video 8. Similarity
Examine your intuitive notions of what makes a "good copy" and then progress toward a more formal definition of similarity. Explore similar triangles and look into some applications of similar triangles, including trigonometry. Go to this unit.

Video 9. Solids
Explore various aspects of solid geometry. Examine platonic solids and why there are a finite number of them. Investigate nets and cross-sections for solids as a way of establishing the relationships between twodimensional and threedimensional geometry. Go to this unit.

Video 10. Classroom Case Studies, K-5
Watch this program in the 10th session for K2 and 35 teachers. Explore how the concepts developed in this course can be applied through case studies of K5 teachers who have adapted their new knowledge to their classrooms. Go to this unit.

Video 11. Classroom Case Studies, 6-8, Part 1
Watch Videos 11 and 12 in the 10th session for grade 68 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 68 teachers (former course participants) who have adapted their new knowledge to their classrooms. Go to this unit.

Video 12. Classroom Case Studies, 6-8, Part 2
Watch Videos 11 and 12 in the 10th session for grade 68 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 68 teachers (former course participants) who have adapted their new knowledge to their classrooms. Go to this unit.